As you said, there are lots of companies that put up car ports. So a specific mfg or contractor in your area would be a local recommendation only, likely.
Sure a pole barn would be a great idea. So would a shop, but presumably those aren’t options for you or you haven’t explored them, as that was not your question.
Issues? Properly assembled and anchored down, there are really no issues to have that I’m aware of. They last virtually forever and keep sun and the wet stuff off of what’s parked under them. That’s about it iMO.
One suggestion is don’t go cheap on the sides. Windward and or sunny sides of car ports, spring for the 3/4 or full siding.